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IGCSE Mathematics – David Rayner – Page 191, Exercise 5 – Bearing
In this exercise, start by drawing a clear diagram.
Q1 A ladder of length 6m leans against a vertical wall so that the base of the ladder is 2m from the wall. Calculate the angle
between the ladder and the wall.
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Q2 A ladder of length 8m rests against a wall so that the angle between the ladder and the wall is 31 . How far is the base of the
ladder from the wall?
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Q3 A ship sails 35km on a bearing of 042 .
(a) How far north has it travelled?
(b) How far east has it travelled?
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Q4 A ship sails 200km on a bearing of 243.7 .
(a) How far south has it travelled?
(b) How far west has it travelled?
Q5 Find TR if PR=10m and QT=7m.
Q6 Find d.
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Q7 An aircraft flies 400km from a point O on a bearing of 025 and then 700km on a bearing of 080 to arrive at B.
(a) How far north of O is B?
(b) How far east of O is B?
(c) Find the distance and bearing of B from O.
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Q8 An aircraft flies 500km on a bearing of 100 and then 600km on a bearing of 160 .
Find the distance and bearing of the finishing point from the starting point.
Q9 From the top of a tower of height 75m, a guard sees two prisoners, both due West of him.
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If the angle of depression of the two prisoners are 10 and 17 . Calculate the distance
between them.
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Q10 A kite is flying at a height of 55m is attached to a string which makes an angle of 55 with the horizontal. What is the length
of the string?
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Q11 A rocket flies 10km vertically, then 20km at an angle of 15 to the vertical and finally 60km at an angle of 26 to the vertical.
Calculate the vertical height of the rocket the third stage.
Q12 A hedgehog wishes to cross a road without being run over. He observes the angle of elevation of a lamp post on the other
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side of the road to be 27 from the edge of the road and 15 from a point 10m back from the road. How wide is the road? If
he can run at 1m/s, how long will he take to cross?
If cars are travelling at 20m/s, how far apart must they be if he is to survive?
Q13 From a point 10m from a vertical wall, the angles of elevation of the bottom and the top of a statue of Sir Isaac Newton, set
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in the wall, are 40 and 52 . Calculate the height of the statue.

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